Attempting to do a improper fraction and a proper fraction is the same as product of 2 proper fractions.
Unlike addition and subtraction of fractions, we DO NOT need to change the denominator to the same common factor.
The only difference is that if the end result becomes an improper fraction, we have to convert/change that improper fraction to a mixed number. That's all.
This is a short post as I have gone through with the class how to attempt multiplication involving fractions. If any one should have any questions, pass them to me during class time, so that I can solve it and post it in this Maths blog for pupils to share.
Mr Xie.
Tuesday, March 31, 2009
Order of Operations.
What are Order of operations?
Simply put, it just means that we have to do certain operations(brackets, multiplication, division ,addition, subtraction) first.
For example,
In this question,
8 x 3 + (5 - 9) x 2. We will need to do the brackets first, followed by the multiplication, finally addition.
How do we know when to do which operation first?
Ever heard of B.O.D.M.A.S?
B= brackets
D= divide
M = multiply
A = Addition
S = subtraction
This BODMAS means that in every equation, we have to follow this "rule" for the computation of the answer or it will not be accurate.
In order to make this more easier to memorise, me and Class5-5 came up with an unique way of memorising BODMAS using this funny sentence.
"Brain of Dinosaurs' Mouse Adding Stars."
Now, let's just hope pupils won't forget this easily when doing order of operations in the future.
Mr Xie.
Simply put, it just means that we have to do certain operations(brackets, multiplication, division ,addition, subtraction) first.
For example,
In this question,
8 x 3 + (5 - 9) x 2. We will need to do the brackets first, followed by the multiplication, finally addition.
How do we know when to do which operation first?
Ever heard of B.O.D.M.A.S?
B= brackets
D= divide
M = multiply
A = Addition
S = subtraction
This BODMAS means that in every equation, we have to follow this "rule" for the computation of the answer or it will not be accurate.
In order to make this more easier to memorise, me and Class5-5 came up with an unique way of memorising BODMAS using this funny sentence.
"Brain of Dinosaurs' Mouse Adding Stars."
Now, let's just hope pupils won't forget this easily when doing order of operations in the future.
Mr Xie.
Thursday, March 26, 2009
Product of two proper fractions.
Class 5-5 learnt the product of 2 proper fractions today.
The first thing I showed the class is this,
Is the above correct? Are the answers the same?
We proceeded to proof this theory by models, which can also be found in their textbook pg 102.
Here's the diagram for easy viewing.
The class was then taught how to use the cancellation method to make multiplication of fraction simpler and easier.
To the class of 5-5, hope that you have learnt somehting new today.
Mr Xie.
The first thing I showed the class is this,
Is the above correct? Are the answers the same?
We proceeded to proof this theory by models, which can also be found in their textbook pg 102.
Here's the diagram for easy viewing.
The class was then taught how to use the cancellation method to make multiplication of fraction simpler and easier.
To the class of 5-5, hope that you have learnt somehting new today.
Mr Xie.
Wednesday, March 25, 2009
Word Problems 2.
Class 5-5 played a short game called ," I have, who has."
The gameplay is fairly simple. Strips of paper with sentences of "I have..., who has..." is randomly passed to each groups.
One groups will read out the first sentence and if the answer of that particular sentence happens to be in your group, you will have to quickly read it out loud!
Here's an example of the activity.
Students that played this game have to make use of their mental ability so they the can answer it quickly and accurately. After exposure to this game, students can also create this game for themselves and play it if they wish to. The trick to creating it is that the last entry of the problem must conincide with the first entry, so that it becomes an infinte loop.
The lesson was ended with me discussing the solutions on their word problems activity.
Oh, in case I forget, here's the shirt for you, Mr "Oh Yock Wu".
Mr Xie.
The gameplay is fairly simple. Strips of paper with sentences of "I have..., who has..." is randomly passed to each groups.
One groups will read out the first sentence and if the answer of that particular sentence happens to be in your group, you will have to quickly read it out loud!
Here's an example of the activity.
Students that played this game have to make use of their mental ability so they the can answer it quickly and accurately. After exposure to this game, students can also create this game for themselves and play it if they wish to. The trick to creating it is that the last entry of the problem must conincide with the first entry, so that it becomes an infinte loop.
The lesson was ended with me discussing the solutions on their word problems activity.
Oh, in case I forget, here's the shirt for you, Mr "Oh Yock Wu".
Mr Xie.
Tuesday, March 24, 2009
Maths Fraction word problems 1
Class 5-5 did problem sums in class today. There is supposed to be an activity for them to play, however, due to time constraints, I had to postphone the activity till tomorrow.
While doing problem sums, this question occured in my mind.
"Does the students understand why they need to show the number sentences, final statements while doing problem solving?" "Did any teacher mention to them before?"
Hence, I grabbed the opportunity to let them be aware of this reasoning.
Firstly, to answer this question, we have to ask ourselves.
"How do we communicate?"
While talking, we communicate in English or Chinese, while writing, we pen our thoughts down. But what about in Mathematics? How are we able to communicate?
Hence, the reason for pupils doing and showing their workings, number sentences, etc... is not to get extra marks which is a possiblity and a bonus for them. The main reason is to communicate. We need to show all these things to "show" whomever is marking our papers/questions that we understand what the problem is asking us. Hence, the most straightforward way to "show" him or her is to work out the solution instead of explaining it in words.
I hope that class 5-5 understands this and will never makes mistakes like omitting any important parts while attempting problem sums.
Mr Xie.
While doing problem sums, this question occured in my mind.
"Does the students understand why they need to show the number sentences, final statements while doing problem solving?" "Did any teacher mention to them before?"
Hence, I grabbed the opportunity to let them be aware of this reasoning.
Firstly, to answer this question, we have to ask ourselves.
"How do we communicate?"
While talking, we communicate in English or Chinese, while writing, we pen our thoughts down. But what about in Mathematics? How are we able to communicate?
Hence, the reason for pupils doing and showing their workings, number sentences, etc... is not to get extra marks which is a possiblity and a bonus for them. The main reason is to communicate. We need to show all these things to "show" whomever is marking our papers/questions that we understand what the problem is asking us. Hence, the most straightforward way to "show" him or her is to work out the solution instead of explaining it in words.
I hope that class 5-5 understands this and will never makes mistakes like omitting any important parts while attempting problem sums.
Mr Xie.
Monday, March 23, 2009
Subtracting Mixed numbers.
Today's lesson is on the subtraaction of mixed numbers. Since pupils already know the concept of subtracting unlike fractions, it's only a matter of time before they attained the concept of subtracting mixed numbers.
Instead of asking them to do the textbook activity, which I believe to be boring to most of the class, I decided to show the class some of the examples that my previous students did. (Which some contains errors in computation).
Up next.... Maths problem sums involving fractions!
Mr Xie.
Instead of asking them to do the textbook activity, which I believe to be boring to most of the class, I decided to show the class some of the examples that my previous students did. (Which some contains errors in computation).
(Click for a larger view)
Up next.... Maths problem sums involving fractions!
Mr Xie.
Sunday, March 15, 2009
Maths Quiz and Mental Sums.
Class 5-5 did a math quiz today. I thought that it was interesting and novel as problems like these doesn't come everyday in mathematics; not when one is still learning concepts of mathematics. I remembered one question in the maths quiz consists of looking for a pattern which is known as a Fibonacci number.
In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci (a contraction of filius Bonaccio, "son of Bonaccio"). The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc.
Now the question is;
Why are we learning all these problem solving when we don't even use them in real life?
The answer to this is not learning to apply. Instead, we are learning to be exposed to different patterns and while constantly looking and solving these patterns, we are using our thinking skills and training our mental ability, so that we are improving on our short-term memory.
Okay... enough of all these theories. Let's have some fun instead.
What I am going to do is I am going to attempt to read your mind. Yes! Reading your mind through your computer screen.
To students of 5-5,
How does this work? Am I really reading your mind? Or is there another possible explanation for this?
You might want to post your "solution" on the tagboard.
Mr Xie.
In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci (a contraction of filius Bonaccio, "son of Bonaccio"). The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc.
Now the question is;
Why are we learning all these problem solving when we don't even use them in real life?
The answer to this is not learning to apply. Instead, we are learning to be exposed to different patterns and while constantly looking and solving these patterns, we are using our thinking skills and training our mental ability, so that we are improving on our short-term memory.
Okay... enough of all these theories. Let's have some fun instead.
What I am going to do is I am going to attempt to read your mind. Yes! Reading your mind through your computer screen.
"Look at this picture, choose a card in your mind and remember it."
Mind reading in progress....15%
...45%
...58%
.....84%
....99%
Done!
The card that you have picked in your mind is gone!
Mind reading in progress....15%
...45%
...58%
.....84%
....99%
Done!
The card that you have picked in your mind is gone!
To students of 5-5,
How does this work? Am I really reading your mind? Or is there another possible explanation for this?
You might want to post your "solution" on the tagboard.
Mr Xie.
Thursday, March 12, 2009
Adding mixed numbers
Today's lesson was interesting in the beginning as pupils were selected to help me 'perform' in a magic trick. Pupils will choose a card randomly and teacher will choose two cards. The sum of the two cards will be the one pupil chose. Jing Ying did the first demonstration and I got it right!
However,Samantha chose a seven... and I got it wrong because I showed 2 cards that were threes... Luckily, I have the solution. By "magically" changing each card into a three-and a half of clubs, I was able to confirm that my prediction is correct. (Which card has 3 and a half anyway? Ah... That's where the magic comes in...)
This activity was immediately followed up by explaining to the class that the card shown above is a mixed number. (A mixed number is a whole number and a proper fraction together).
To add two mixed numbers together, first we add the proper fractions together first, followed by the whole numbers. Bear in mind that while adding fractions, we must always find a common multiple before attempting the equation, or else the solution for the problem will be inaccurate.
After teaching how to add, (It's almost the same as adding unlike fractions!), the class played a game in pairs, using their calculator and the "RAN" button. I hope the class enjoyed the short activity and appreciate the effort of me thinking of the game for them.
Mr Xie.
However,Samantha chose a seven... and I got it wrong because I showed 2 cards that were threes... Luckily, I have the solution. By "magically" changing each card into a three-and a half of clubs, I was able to confirm that my prediction is correct. (Which card has 3 and a half anyway? Ah... That's where the magic comes in...)
Here's the image of the card...Now you have witnessed the incredible....
This activity was immediately followed up by explaining to the class that the card shown above is a mixed number. (A mixed number is a whole number and a proper fraction together).To add two mixed numbers together, first we add the proper fractions together first, followed by the whole numbers. Bear in mind that while adding fractions, we must always find a common multiple before attempting the equation, or else the solution for the problem will be inaccurate.
After teaching how to add, (It's almost the same as adding unlike fractions!), the class played a game in pairs, using their calculator and the "RAN" button. I hope the class enjoyed the short activity and appreciate the effort of me thinking of the game for them.
Mr Xie.
Wednesday, March 11, 2009
Converting fractions to decimals.
Today pupils learnt about the conversion of fractions to decimals.
Why do we need to learn this mathematical concept?
This is one of the tasks that pupils did. Some commented that they did not know what to write and I hope that they are able to realise it soon.
(Answer will NOT be revealed here)
Basically, there are two methods of converting fractions to decimals.
One - The simple way.
Change the denominator to 10, 100 or 1000.
From there on, the numerator gets changed as well.
After which, decimals can be found quite easily as it is a matter of "shifting" the decimal point.
(Note that the value '8' can be converted to 1000, simply by just multiplying it by 125)
But what happens if the denominator can't be converted to 10, 100 or 1000?
Then you will have to use the second method, which is...
TWO - The troublesome but effective way.
Do it the long division way.
For example, find the decimal of the fraction,three-quarters, (3/4). You take 3 divided by 2 and work out the solution. Bear in mind that the worked solution can be very long. One hint is to read the instruction. If the instruction states that you should round off to 2 decimal places, working the solution to just 3 decimal places will be good enough.
Confused?
The only way not to be is to practice, practice and more practice.
Hope class 5-5 will be able to handle all sorts of fractions as this is going to be a loooooooooong topic.
Mr Xie.
Why do we need to learn this mathematical concept?
This is one of the tasks that pupils did. Some commented that they did not know what to write and I hope that they are able to realise it soon.
(Answer will NOT be revealed here)
Basically, there are two methods of converting fractions to decimals.
One - The simple way.
Change the denominator to 10, 100 or 1000.
From there on, the numerator gets changed as well.
After which, decimals can be found quite easily as it is a matter of "shifting" the decimal point.
(Note that the value '8' can be converted to 1000, simply by just multiplying it by 125)
But what happens if the denominator can't be converted to 10, 100 or 1000?
Then you will have to use the second method, which is...
TWO - The troublesome but effective way.
Do it the long division way.
For example, find the decimal of the fraction,three-quarters, (3/4). You take 3 divided by 2 and work out the solution. Bear in mind that the worked solution can be very long. One hint is to read the instruction. If the instruction states that you should round off to 2 decimal places, working the solution to just 3 decimal places will be good enough.
Confused?
The only way not to be is to practice, practice and more practice.
Hope class 5-5 will be able to handle all sorts of fractions as this is going to be a loooooooooong topic.
Mr Xie.
Tuesday, March 10, 2009
Relationship between fractions and division.
Today's lesson on Mathematics became a sharing session. All students were 'transformed' into pupils with good values and lots of chocolate bar(fake of course) and began sharing parts of it with one another.
The lesson began by teaching pupils how to divide the chocolate into an accurate number of parts.
I wonder if students saw and understood the pattern behind this 'sharing'.
The trick is to first know how many person one is sharing the chocolate first.
From there on, the chocolate is divided into the number of persons in the group.
Following on, each person will receive a small piece and the fraction of the number of pieces can be "seen" very easily.
After which, pupils are grouped and given strips of paper to divide accordingly. I am glad that most groups made the effort to try and divide. (For those who didn't, you know who you are).
Eventually, most of the groups got the answer.
Hence, the fraction each person will receive is 3/4. (three-quarters).
For class 5-5 pupils.
Can you all see the pattern? What happens if the number of chocolate bars is more than the amount of persons sharing?
(E.g. If I were to share 5 chocolate bars with 4 persons, what fraction of the chocolate bar would each receive?)
Would one derive at a mixed number?
What do you think?
Mr.Xie.
The lesson began by teaching pupils how to divide the chocolate into an accurate number of parts.
I wonder if students saw and understood the pattern behind this 'sharing'.
The trick is to first know how many person one is sharing the chocolate first.
From there on, the chocolate is divided into the number of persons in the group.
Following on, each person will receive a small piece and the fraction of the number of pieces can be "seen" very easily.
After which, pupils are grouped and given strips of paper to divide accordingly. I am glad that most groups made the effort to try and divide. (For those who didn't, you know who you are).
Eventually, most of the groups got the answer.
An example can be seen from this pupil's journal.
Hence, the fraction each person will receive is 3/4. (three-quarters).For class 5-5 pupils.
Can you all see the pattern? What happens if the number of chocolate bars is more than the amount of persons sharing?
(E.g. If I were to share 5 chocolate bars with 4 persons, what fraction of the chocolate bar would each receive?)
Would one derive at a mixed number?
What do you think?
Mr.Xie.
Friday, March 6, 2009
Subtracting Unlike Fractions.
Today's lesson was on "How to subtract unlike fractions".
The first task began by asking pupils to group 24 marbles equally.
Here are some of the student's way of grouping 24 marbles written on their mini-journal.
The first task began by asking pupils to group 24 marbles equally.
Here are some of the student's way of grouping 24 marbles written on their mini-journal.
The objective of this activity is to lead them to understand that though fractions can be different, the total value remains the same. This goes to show that by manipulating fraction numbers, we are only manipulating their numerators and denominators and not their value.
Here's another "proof" shown below.
Understanding this concept will help students remember how to manipulate fractions when dealing with unlike fractions.
Students attempting the questions of adding and subtracting unlike fractions..
I was pleased to hear another student coming up with another variation of converting the denominators to a common multiple. (shown above). I quickly used the chance to explain that though using a different multiple may be different initially, the end result will be the same. I was so excited in proving this that I nearly forget to mention that one must always simplify fractions into simplest form whenever possible.
Guess I better inform the class for the next lesson.
Mr Xie.
Thursday, March 5, 2009
How NOT to do a PowerPoint Presentation.
Integrated Project Work (IPW) for class 5-5 has officially ended.
After listening to some of their presentations, I decided to do up some PowerPoint slides to show pupils the common mistakes when presenting with PowerPoint slides.
This is the first time I included humour into a short sharing with the pupils.
I'm glad that pupils were laughing and enjoying the presentation.
I hope that pupils have not only enjoyed the presentation, they are also able to remember and not to include the same mistakes again while presenting in the future.
Mr Xie.
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